Ok, I've heard it explained a few times so I'll try and re-expklain best I can. It is known that we are dear to ourselvse, therefore we know that we wish no harm upon ourselves. We should realize that other beings feel the same way about themselves.

It's kind of like "do unto others." Or "we're all in the same samsaric boat." Or in negative terms, if you would do something harmful to another person, they might say "well how would YOU like it if I did that to you?" You wouldn't like it - so don't do it to other people.

here are the stanzas. Can anyone help understanding the meaning of the conclusion?

Searching all directions
with one's awareness,
one finds no one dearer
than oneself.
In the same way, others
are fiercely dear to themselves.So one should not hurt others
if one loves oneself.

I think those verses require the ability and the will to empathize with others. If that is not given, there is no "logic" to be found in them. In such cases another motive for not hurting others is required instead, maybe the prospect of punishment or a bad rebirth.

"So one should not hurt others if one loves oneself", looked at from another perspective, also reflects the way in which actions which are intended to harm others, are rooted in greed, aversion or delusion, and are thus harmful to one's self. See for example...

The Golden Rule, do unto others as you would be done by, is the moral cornerstone of most religions. Christain, Buddhist, Jewish and many more: http://www.religioustolerance.org/reciproc.htm. The Buddha states it too in a number of places and ways but I think he also adds to it with an exliantion of why compassion is good and greed or deceit bad.

I think that the real mystery about The Golden Rule isn't its logic but this:

If every religion claims to adhere to The Golden Rule then why is it not adhered to between the world's religions?

well my point is rather that there is a missing link in the conclusion, the reality underlying the word "so" between 'loving oneself' and 'not hurting others'. This feels strange to me because the Buddha never misses any link in a detailed explanation. This explanation starts like a detailed one, and suddenly jumps to the conclusion at the end. I was wondering if there is a way to understand this statement without making any assumption, or if there would be a mistranslation, or if simply at this time the Buddha did not explain fully his (seemingly detailed) statement.

Searching all directions
with one’s awareness,
one finds no one dearer
than oneself.
In the same way, others
are fiercely dear to themselves.
So one should not hurt others
if one loves oneself.

In other words, true self‐love requires an appreciation that others feel self‐love, too. This principle works in two ways: First, you recognize that if your happiness depends on the misery of others it won’t last, for they’ll do whatever they can to destroy that happiness. Your long‐term happiness thus has to take into account the long‐term happiness of others. Second, in a less calculating way, you recognize what we all have in common. If you take your own self‐love seriously, you have to respect the self‐love of others. In this way, compassion is based not on a sense of your superiority to those who are suffering but on a sense of mutual respect—a respect solidly based in your own self‐interest.

I don't think this is an appeal to logic but to sympathy. reflecting on the first two statements will (in most cases) bring about the arising of fellow feeling and that "logicically" leads to the conclusion, If you want a logical and more selfish augment for not harming others it would be something like this.

you wish for happiness
harming others leads to unhappiness
therefore do not harm others.

Searching all directions
with one’s awareness,
one finds no one dearer
than oneself.
In the same way, others
are fiercely dear to themselves.
So one should not hurt others
if one loves oneself.

In other words, true self‐love requires an appreciation that others feel self‐love, too. This principle works in two ways: First, you recognize that if your happiness depends on the misery of others it won’t last, for they’ll do whatever they can to destroy that happiness. Your long‐term happiness thus has to take into account the long‐term happiness of others. Second, in a less calculating way, you recognize what we all have in common. If you take your own self‐love seriously, you have to respect the self‐love of others. In this way, compassion is based not on a sense of your superiority to those who are suffering but on a sense of mutual respect—a respect solidly based in your own self‐interest.

"Bhikkhus, once there was an acrobat who set up his bamboo pole and called to his student, saying, "Come here and climb the pole and stand on my shoulders," and the pupil did as he was told.

Then the bamboo acrobat said to his pupil, "Now, you take good care of me and I'll take good care of you. By watching over and protecting each other like this, we will show off our skills, get a good fee, and safely descend from the bamboo pole."

At these words, the pupil said to his teacher, "Teacher, I don't think I can do that. You look after yourself and I will look after myself. If we both watch and protect ourselves then we will be able to show our art, get a good fee, and safely descend the bamboo pole."

The Blessed One said, "That was the correct thing to do in that case: Just as that pupil spoke to his master, when thinking, 'I will protect myself,' you must be mindful, and when thinking, 'I will protect others,' you must also be mindful.

And how is it that while protecting yourself you protect others? By earnest practice, development, training, and making the most of it. In this way, when you protect yourself, you protect others. And how do you protect others by protecting yourself? By proper resolve {chanda), by non-violence, by
possessing a heart of loving-kindness and compassion. In this way, protecting others, you protect yourself.

Bhikkhus, when thinking, 'I will protect myself,' you must be mindful. When thinking, 'I will protect others,' you must also be mindful. In this way, protecting yourself can be called protecting others, and protecting others can be called protecting yourself."